Details

analyze1.1s (24.6%)

Algorithm

1×

Search

True	Other	False	Iter
0%	48.6%	51.4%	0
0%	48.6%	51.4%	1
24.3%	24.3%	51.4%	2
24.3%	24.3%	51.4%	3
30.4%	18.2%	51.4%	4
30.4%	18.2%	51.4%	5
33.4%	15.2%	51.4%	6
33.4%	15.2%	51.4%	7
34.6%	14.1%	51.4%	8
34.8%	13.9%	51.4%	9
35.4%	13.2%	51.4%	10
35.6%	13.1%	51.4%	11
35.9%	12.7%	51.4%	12
36%	12.6%	51.4%	13
36.2%	12.4%	51.4%	14

Compiler

Compiled 28 to 20 computations (28.6% saved)

sample2.0s (43.6%)

Results

916.0ms	6310×	body	128	valid
460.0ms	761×	body	2048	valid
270.0ms	516×	body	1024	valid
217.0ms	314×	body	4096	valid
87.0ms	242×	body	512	valid
27.0ms	113×	body	256	valid

Compiler

Compiled 75 to 54 computations (28% saved)

simplify11.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

9×	`fma-def_binary64`
6×	`*-commutative_binary64`
2×	`+-commutative_binary64`
2×	`associate-/l*_binary64`
2×	`distribute-lft-in_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	15	24
1	31	24
2	41	22
3	48	22
4	50	22
5	52	22
6	53	22

Stop Event

1×

saturated

Counts

1 → 2

prune3.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	2	1	3

Error

12.9b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	12.9b	(sqrt.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 4 (.f64 p p))))) 1/2))

Compiler

Compiled 68 to 48 computations (29.4% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 4 (.f64 p p))))) 1/2))
✓	0.0b	(.f64 4 (.f64 p p))
✓	0.8b	(fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 4 (.f64 p p))))) 1/2)
✓	14.2b	(sqrt.f64 (fma.f64 x x (.f64 4 (.f64 p p))))

series51.0ms (1.1%)

Counts

4 → 84

Calls

4 calls:

22.0ms	(sqrt.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 4 (.f64 p p))))) 1/2))
17.0ms	(fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 4 (.f64 p p))))) 1/2)
9.0ms	(sqrt.f64 (fma.f64 x x (.f64 4 (.f64 p p))))
2.0ms	(.f64 4 (.f64 p p))

rewrite49.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

544×	`log-prod_binary64`
204×	`expm1-udef_binary64`
204×	`log1p-udef_binary64`
190×	`log-pow_binary64`
154×	`prod-diff_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	62
1	247	44
2	2892	44

Stop Event

1×	node limit

Counts

4 → 101

Calls

4 calls:

47.0ms	(sqrt.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 4 (.f64 p p))))) 1/2))
47.0ms	(.f64 4 (.f64 p p))
47.0ms	(fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 4 (.f64 p p))))) 1/2)
47.0ms	(sqrt.f64 (fma.f64 x x (.f64 4 (.f64 p p))))

simplify40.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

580×	`associate-/l*_binary64`
515×	`associate-/r*_binary64`
431×	`fma-def_binary64`
304×	`cancel-sign-sub-inv_binary64`
210×	`fma-neg_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	154	1801
1	497	1749
2	1747	1656

Stop Event

1×	node limit

Counts

185 → 188

prune139.0ms (3%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	183	5	188
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	184	5	189

Error

2.5b

Counts

189 → 5

Alt Table

Status	Error	Program
	54.4b	(/.f64 (neg.f64 p) x)
▶	12.8b	(pow.f64 (fma.f64 1/2 (/.f64 x (hypot.f64 x (*.f64 p 2))) 1/2) 1/2)
	13.3b	(-.f64 (exp.f64 (log1p.f64 (sqrt.f64 (fma.f64 1/2 (/.f64 x (hypot.f64 x (*.f64 p 2))) 1/2)))) 1)
	55.6b	(sqrt.f64 (fma.f64 (/.f64 (pow.f64 p 4) (pow.f64 x 4)) -3 (fma.f64 (/.f64 p x) (/.f64 p x) (/.f64 (*.f64 (pow.f64 p 6) 10) (pow.f64 x 6)))))
	50.9b	(sqrt.f64 (*.f64 (/.f64 p x) (/.f64 p x)))

Compiler

Compiled 3805 to 2797 computations (26.5% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(pow.f64 (fma.f64 1/2 (/.f64 x (hypot.f64 x (*.f64 p 2))) 1/2) 1/2)
✓	0.8b	(fma.f64 1/2 (/.f64 x (hypot.f64 x (*.f64 p 2))) 1/2)

series44.0ms (1%)

Counts

2 → 48

Calls

2 calls:

26.0ms	(pow.f64 (fma.f64 1/2 (/.f64 x (hypot.f64 x (*.f64 p 2))) 1/2) 1/2)
18.0ms	(fma.f64 1/2 (/.f64 x (hypot.f64 x (*.f64 p 2))) 1/2)

rewrite46.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

909×	`log1p-expm1-u_binary64`
909×	`expm1-log1p-u_binary64`
111×	`prod-diff_binary64`
102×	`add-sqr-sqrt_binary64`
96×	`add-log-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	30
1	212	30
2	2505	30

Stop Event

1×	node limit

Counts

2 → 46

Calls

2 calls:

45.0ms	(pow.f64 (fma.f64 1/2 (/.f64 x (hypot.f64 x (*.f64 p 2))) 1/2) 1/2)
45.0ms	(fma.f64 1/2 (/.f64 x (hypot.f64 x (*.f64 p 2))) 1/2)

simplify30.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

798×	`times-frac_binary64`
376×	`associate-/l*_binary64`
367×	`associate-/r*_binary64`
261×	`fma-def_binary64`
195×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	115	1326
1	361	1270
2	1211	1146

Stop Event

1×	node limit

Counts

94 → 101

prune80.0ms (1.7%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	100	1	101
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	100	6	106

Error

1.8b

Counts

106 → 6

Alt Table

Status	Error	Program
✓	12.8b	(pow.f64 (fma.f64 1/2 (/.f64 x (hypot.f64 x (*.f64 p 2))) 1/2) 1/2)
	54.1b	(exp.f64 (.f64 1/2 (+.f64 (.f64 2 (log.f64 (/.f64 -1 x))) (log.f64 (pow.f64 p 2)))))
	54.4b	(/.f64 (neg.f64 p) x)
▶	13.3b	(-.f64 (exp.f64 (log1p.f64 (sqrt.f64 (fma.f64 1/2 (/.f64 x (hypot.f64 x (*.f64 p 2))) 1/2)))) 1)
	55.6b	(sqrt.f64 (fma.f64 (/.f64 (pow.f64 p 4) (pow.f64 x 4)) -3 (fma.f64 (/.f64 p x) (/.f64 p x) (/.f64 (*.f64 (pow.f64 p 6) 10) (pow.f64 x 6)))))
	50.9b	(sqrt.f64 (*.f64 (/.f64 p x) (/.f64 p x)))

Compiler

Compiled 2338 to 1744 computations (25.4% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (fma.f64 1/2 (/.f64 x (hypot.f64 x (*.f64 p 2))) 1/2))
✓	0.5b	(log1p.f64 (sqrt.f64 (fma.f64 1/2 (/.f64 x (hypot.f64 x (*.f64 p 2))) 1/2)))
	0.8b	(fma.f64 1/2 (/.f64 x (hypot.f64 x (*.f64 p 2))) 1/2)
✓	1.0b	(-.f64 (exp.f64 (log1p.f64 (sqrt.f64 (fma.f64 1/2 (/.f64 x (hypot.f64 x (*.f64 p 2))) 1/2)))) 1)

series85.0ms (1.9%)

Counts

3 → 72

Calls

3 calls:

40.0ms

(-.f64 (exp.f64 (log1p.f64 (sqrt.f64 (fma.f64 1/2 (/.f64 x (hypot.f64 x (*.f64 p 2))) 1/2)))) 1)

27.0ms

(log1p.f64 (sqrt.f64 (fma.f64 1/2 (/.f64 x (hypot.f64 x (*.f64 p 2))) 1/2)))

18.0ms

(sqrt.f64 (fma.f64 1/2 (/.f64 x (hypot.f64 x (*.f64 p 2))) 1/2))

rewrite56.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

289×	`prod-diff_binary64`
221×	`log1p-udef_binary64`
220×	`expm1-udef_binary64`
195×	`log-pow_binary64`
147×	`fma-def_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	50
1	273	50
2	3184	50

Stop Event

1×	node limit

Counts

3 → 110

Calls

3 calls:

53.0ms

(sqrt.f64 (fma.f64 1/2 (/.f64 x (hypot.f64 x (*.f64 p 2))) 1/2))

53.0ms

(log1p.f64 (sqrt.f64 (fma.f64 1/2 (/.f64 x (hypot.f64 x (*.f64 p 2))) 1/2)))

53.0ms

(-.f64 (exp.f64 (log1p.f64 (sqrt.f64 (fma.f64 1/2 (/.f64 x (hypot.f64 x (*.f64 p 2))) 1/2)))) 1)

simplify52.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

889×	`fma-def_binary64`
431×	`cancel-sign-sub-inv_binary64`
217×	`sub-neg_binary64`
195×	`fma-neg_binary64`
153×	`distribute-neg-frac_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	171	2906
1	570	2696
2	2540	2552

Stop Event

1×	node limit

Counts

182 → 128

prune140.0ms (3%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	184	0	184
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	184	6	190

Error

1.8b

Counts

190 → 6

Alt Table

Status	Error	Program
✓	12.8b	(pow.f64 (fma.f64 1/2 (/.f64 x (hypot.f64 x (*.f64 p 2))) 1/2) 1/2)
	54.1b	(exp.f64 (.f64 1/2 (+.f64 (.f64 2 (log.f64 (/.f64 -1 x))) (log.f64 (pow.f64 p 2)))))
	54.4b	(/.f64 (neg.f64 p) x)
✓	13.3b	(-.f64 (exp.f64 (log1p.f64 (sqrt.f64 (fma.f64 1/2 (/.f64 x (hypot.f64 x (*.f64 p 2))) 1/2)))) 1)
	55.6b	(sqrt.f64 (fma.f64 (/.f64 (pow.f64 p 4) (pow.f64 x 4)) -3 (fma.f64 (/.f64 p x) (/.f64 p x) (/.f64 (*.f64 (pow.f64 p 6) 10) (pow.f64 x 6)))))
▶	50.9b	(sqrt.f64 (*.f64 (/.f64 p x) (/.f64 p x)))

Compiler

Compiled 5274 to 4185 computations (20.6% saved)

localize4.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.3b	(*.f64 (/.f64 p x) (/.f64 p x))
✓	17.9b	(sqrt.f64 (*.f64 (/.f64 p x) (/.f64 p x)))

series26.0ms (0.6%)

Counts

2 → 48

Calls

2 calls:

21.0ms	(*.f64 (/.f64 p x) (/.f64 p x))
5.0ms	(sqrt.f64 (*.f64 (/.f64 p x) (/.f64 p x)))

rewrite39.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

567×	`log1p-expm1-u_binary64`
567×	`expm1-log1p-u_binary64`
286×	`log-prod_binary64`
142×	`pow2_binary64`
103×	`egg-rr`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	11
1	129	11
2	1599	11

Stop Event

1×	node limit

Counts

2 → 103

Calls

2 calls:

37.0ms	(*.f64 (/.f64 p x) (/.f64 p x))
37.0ms	(sqrt.f64 (*.f64 (/.f64 p x) (/.f64 p x)))

simplify36.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

671×	`times-frac_binary64`
650×	`unswap-sqr_binary64`
326×	`associate-/l*_binary64`
213×	`associate-/r*_binary64`
150×	`associate-/l/_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	352
1	22	352
2	42	352
3	106	352
4	434	352
5	3292	352
6	4926	352

Stop Event

1×	node limit

Counts

151 → 107

prune33.0ms (0.7%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	106	1	107
Fresh	1	2	3
Picked	1	0	1
Done	0	2	2
Total	108	5	113

Error

0.0b

Counts

113 → 5

Alt Table

Status	Error	Program
	52.3b	(/.f64 p x)
	55.6b	(sqrt.f64 (fma.f64 (/.f64 (pow.f64 p 4) (pow.f64 x 4)) -3 (fma.f64 (/.f64 p x) (/.f64 p x) (/.f64 (*.f64 (pow.f64 p 6) 10) (pow.f64 x 6)))))
	54.4b	(/.f64 (neg.f64 p) x)
✓	12.8b	(pow.f64 (fma.f64 1/2 (/.f64 x (hypot.f64 x (*.f64 p 2))) 1/2) 1/2)
✓	13.3b	(-.f64 (exp.f64 (log1p.f64 (sqrt.f64 (fma.f64 1/2 (/.f64 x (hypot.f64 x (*.f64 p 2))) 1/2)))) 1)

Compiler

Compiled 969 to 471 computations (51.4% saved)

regimes385.0ms (8.4%)

Accuracy

Total 5.4b remaining (99.2%)

Threshold costs 0b (0%)

Counts

66 → 2

Compiler

Compiled 6514 to 5152 computations (20.9% saved)

bsearch2.0ms (0%)

Compiler: Compiled 14 to 9 computations (35.7% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

3×	`*-commutative_binary64`
1×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	4294967295
1	32	4294967295

Stop Event

1×

saturated

end87.0ms (1.9%)

Compiler: Compiled 150 to 105 computations (30% saved)

Details

analyze1.1s (24.6%)

sample2.0s (43.6%)

simplify11.0ms (0.2%)

prune3.0ms (0.1%)

localize9.0ms (0.2%)

series51.0ms (1.1%)

rewrite49.0ms (1.1%)

simplify40.0ms (0.9%)

prune139.0ms (3%)

localize7.0ms (0.1%)

series44.0ms (1%)

rewrite46.0ms (1%)

simplify30.0ms (0.6%)

prune80.0ms (1.7%)

localize10.0ms (0.2%)

series85.0ms (1.9%)

rewrite56.0ms (1.2%)

simplify52.0ms (1.1%)

prune140.0ms (3%)

localize4.0ms (0.1%)

series26.0ms (0.6%)

rewrite39.0ms (0.8%)

simplify36.0ms (0.8%)

prune33.0ms (0.7%)

regimes385.0ms (8.4%)

bsearch2.0ms (0%)

simplify2.0ms (0%)

end87.0ms (1.9%)

Profiling